AHA-BUCH

Mean Field Models for Spin Glasses

Volume II: Advanced Replica-Symmetry and Low Temperature
 Previously published in hardcover
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ISBN-13:
9783642270949
Einband:
Previously published in hardcover
Erscheinungsdatum:
21.11.2013
Seiten:
644
Autor:
Michel Talagrand
Gewicht:
942 g
Format:
233x156x38 mm
Sprache:
Englisch
Beschreibung:

This is a revised, updated and enlarged edition of Volume II of the author's book "Spin Glasses: A Challenge for Mathematicians" designed to introduce this exciting work to the math-minded reader, in a rigorous manner requiring no knowledge of any physics.
Completely rewritten, updated and enlarged edition of Talagrand's Ergebnisse Vol. 46: "Spin Glasses: A Challenge for Mathematicians" (2003) in two volumesWill bring the reader with no previous knowledge of Spin Glasses to the frontier of current researchThe only fully rigorous treatise of this scale on the subjectThe present second volume contains a large amount of new results obtained after the publication of the first edition.
Part I. Advanced Replica-Symmetry. - The Gardener Formula for the sphere. - The Gardener Formula for the Discrete Cube. - The Hopfield Model. - The SK Model Without External Field. - Part II. Low Temperature. - The Ghirlanda-Guerra Identities. - The High-Temperature Region of the SK Model. - The Parisi Formula. - The Parisi Solution. - The p -spin Interaction Model. - Appendix: Elements of Probability Theory. - References. - Index.
This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians" in two volumes (this is the 2nd volume). In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The present Volume II contains a considerable amount of new material, in particular all the fundamental low-temperature results obtained after the publication of the first edition.